On the lacunary convergent series representations for zeta(n)

作者：Dai, Li-Xia; Pan, Hao^*; Xu, Ji-Zhen

来源：International Journal of Mathematics, 2018, 29(6): 1850038.

DOI：10.1142/S0129167X18500386

• Bernoulli number
• Riemann zeta-function
• Lerch transcendent

We prove some lacunary convergent series representations for zeta(n). For example, we prove that
zeta(7) = Sigma(infinity)(k=2) (-1)(k) (2 pi)(6k)/(6k + 3)! . B6k-6/k-1 + pi(6)/945 (1+1/2 + ... + 1/9 - log (2 pi)),
where B-n are the nth Bernoulli numbers.

• 出版日期2018-6
• 单位南京师范大学; 南京财经大学